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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Conformal circles and parametrizations of curves in conformal manifolds


Authors: T. N. Bailey and M. G. Eastwood
Journal: Proc. Amer. Math. Soc. 108 (1990), 215-221
MSC: Primary 53C22; Secondary 58G30, 83C60
MathSciNet review: 994771
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Abstract | References | Similar Articles | Additional Information

Abstract: We give a simple ODE for the conformal circles on a conformal manifold, which gives the curves together with a family of preferred parametrizations. These parametrizations endow each conformal circle with a projective structure. The equation splits into two pieces, one of which gives the conformal circles independent of any parameterization, and another which can be applied to any curve to generate explicitly the projective structure which it inherits from the ambient conformal structure [1].

We discuss briefly the use of conformal circles to give preferred coordinates and metrics in the neighborhood of a point, and sketch the relationship with twistor theory in the case of dimension four.


References [Enhancements On Off] (What's this?)

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  • [2] H. Friedrich and B. G. Schmidt, Conformal geodesics in general relativity, Proc. Roy. Soc. London Ser. A 414 (1987), no. 1846, 171–195. MR 919722 (89b:83041)
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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-0994771-7
PII: S 0002-9939(1990)0994771-7
Article copyright: © Copyright 1990 American Mathematical Society